Displaying similar documents to “On the Wold-type decomposition of a pair of commuting isometries”

On a decomposition for pairs of commuting contractions

Zbigniew Burdak (2007)

Studia Mathematica

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A new decomposition of a pair of commuting, but not necessarily doubly commuting contractions is proposed. In the case of power partial isometries a more detailed decomposition is given.

Componentwise and Cartesian decompositions of linear relations

S. Hassi, H. S. V. de Snoo, F. H. Szafraniec

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Let A be a, not necessarily closed, linear relation in a Hilbert space ℌ with a multivalued part mul A. An operator B in ℌ with ran B ⊥ mul A** is said to be an operator part of A when A = B +̂ ({0} × mul A), where the sum is componentwise (i.e. span of the graphs). This decomposition provides a counterpart and an extension for the notion of closability of (unbounded) operators to the setting of linear relations. Existence and uniqueness criteria for an operator part are established...

Wold-type extension for N-tuples of commuting contractions

Marek Kosiek, Alfredo Octavio (1999)

Studia Mathematica

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Let (T1,…,TN) be an N-tuple of commuting contractions on a separable, complex, infinite-dimensional Hilbert space ℋ. We obtain the existence of a commuting N-tuple (V1,…,VN) of contractions on a superspace K of ℋ such that each V j extends T j , j=1,…,N, and the N-tuple (V1,…,VN) has a decomposition similar to the Wold-von Neumann decomposition for coisometries (although the V j need not be coisometries). As an application, we obtain a new proof of a result of Słociński (see [9])